Nonlinear interpolation, particularly involute interpolation, in numerical control systems is highly required for the machining of gears, pump vanes, or the like. Generally, an involute curve is interpolated by a computer or an NC program generator which is separate from a numerical control system, producing linear data on a tape, and a workpiece is machined by the numerical control system using the tape.
The applicants have filed Japanese Patent Application No. 62-157302 (Japanese Laid-Open Patent Publication No. 64-2106) on an involute interpolation speed control method. According to the disclosed method, an involute curve is simply interpolated in a numerical control system, and the speed in a tangential direction is held constant irrespective of the angle.
In the proposed involute interpolation speed method, the coordinates of a point on an involute curve are given by: EQU X=R{cos(.theta.+.theta.1)+.theta.sin(.theta.+.theta.l)}+Xo EQU Y=R{sin(.theta.+.theta.1)-.theta.cos(.theta.+.theta.1)}+Yo,
the angle .theta. is increased in a range from .theta.=(.theta.2-.theta.1) to .theta.=(.theta.3-.theta.1) by an increment: EQU .theta.n+1=.theta.n+K/(R.multidot..theta.),
a point Xn+1, Yn+1 corresponding to the increased angle is determined according to the above equations, and the difference between the points is determined, thus interpolating the involute curve.
The speed in a tangential direction can be rendered constant by selecting the increment of .theta. to be of a value which is reduced in inverse proportion to the angle, i.e., a value of K/(R.multidot..theta.).
In the vicinity of the base circle for the involute curve, i.e., a region where the radius of curvature of the involute curve is relatively small, however, a cutter would be subjected to a large load, making the machined surface defective if the workpiece were machined at a feed speed commanded by the program.